We have experimented with several approaches to penalized matrix decomposition (PMD), and found that an iterative rank-one deflation approach similar to the method described in [1]} works well. We begin by standardizing the data within a patch: for each pixel, we subtract the mean and normalize by an estimate of the noise variance within each pixel; the noise variance is estimated using the frequency-domain method described in [2]}, which exploits the fact that the signal and noise power are spectrally separated in movies with sufficiently high frame rates. After this normalization we can model the noise \(\mathbf {E}\)  as roughly spatially and temporally homogeneous. Denote this standardized data matrix within a patch as \(\mathbf {Y_0}\) , and Frobenius norm as \(||.||_F\) . Then at the \(k^{th}\)  iteration PMD extracts the best rank-one approximation \(\mathbf {u}_k\mathbf {v}_k^T\)  to the current residual \(\mathbf {R}_k = \mathbf {Y_0} - \sum _{n=1}^{k-1} \mathbf {u}_n\mathbf {v}_n^T\) , as determined by the objective
\((\mathbf {u}_k, \mathbf {v}_k) = \underset{\mathbf {u}, \mathbf {v}}{\arg \min } ~ || \mathbf {R}_k - \mathbf {u} \mathbf {v}^T ||_F \hspace{10.0pt} \text{subject to} \hspace{10.0pt}P_{spatial}(\mathbf {u}) \le c_{1}^k,\ P_{temporal}(\mathbf {v}) \le c_{2}^{k}, \) 
